The document discusses different forms of energy including kinetic energy, heat, electricity, electromagnetic waves, and mass. It explains that energy can be transformed from one form to another but cannot be created or destroyed. Mass is described as a form of energy according to Einstein's equation E=mc2. Examples are provided to illustrate concepts such as kinetic energy, electromagnetic frequency, and how a small amount of mass contains a huge amount of potential energy.

1. Energy
Kardan University
Uploaded BY: Engr.Ahmad Sameer Nawab

2. What is Energy
From Merriam Webster:
Energy: The capacity for doing work (or to produce heat)
What are some forms/types of energy?
1. Energy of motion (kinetic energy) 
2. Heat
3. Electricity 
4. Electromagnetic waves - like visible light, x-rays, UV rays,
microwaves, etc 
5. Mass 
Huh, what do you mean mass is a form of energy?
We’ll get to this later….
 The thing about energy is that it cannot be created or
destroyed, it can only be transformed from one form into another
From Merriam Webster:
Energy: The capacity for doing work (or to produce heat)
What are some forms/types of energy?
1. Energy of motion (kinetic energy) 
2. Heat
3. Electricity 
4. Electromagnetic waves - like visible light, x-rays, UV rays,
microwaves, etc 
5. Mass 
Huh, what do you mean mass is a form of energy?
We’ll get to this later….
 The thing about energy is that it cannot be created or
destroyed, it can only be transformed from one form into another

3. Energy Conservation
Like momentum, energy is a conserved quantity.
This provides powerful constraints on what can and cannot happen
in nature.
This is an extremely important concept, and we will come back to
this over and over throughout the remainder of the course.

4. Kinetic Energy – Energy of Motion
Kinetic energy (KE) refers to the energy associated with the motion
of an object. The kinetic energy is simply:
KE = (½)mv2
where
m = mass in [kg], and
v = velocity of object in [m/sec]
What are the units of KE?
[KE] = [mass] [velocity]2
= [kg*m2
/s2
] == [Joule] or just, [J]
A Joule is a substantial amount of energy!
Kinetic energy (KE) refers to the energy associated with the motion
of an object. The kinetic energy is simply:
KE = (½)mv2
where
m = mass in [kg], and
v = velocity of object in [m/sec]
What are the units of KE?
[KE] = [mass] [velocity]2
= [kg*m2
/s2
] == [Joule] or just, [J]
A Joule is a substantial amount of energy!

5. Energy
 The unit, [Joules] applies to all forms of energy, not just KE.
 As we’ll see later, there are sometimes more convenient units
to use for energy.
 You have probably heard of the unit “Watt”. For example,
a 100 Watt light bulb?
A Watt [W] is simply energy usage per unit time, or [J/s].
 So, 100 [W] means the bulb uses 100 [J] per second!
 How many [J] are used by a 100 [W] bulb in 2 minute?
A) 200 [J] B) 1200 [J] C) 12000 [J] D) 2000 [J]
 The unit, [Joules] applies to all forms of energy, not just KE.
 As we’ll see later, there are sometimes more convenient units
to use for energy.
 You have probably heard of the unit “Watt”. For example,
a 100 Watt light bulb?
A Watt [W] is simply energy usage per unit time, or [J/s].
 So, 100 [W] means the bulb uses 100 [J] per second!
 How many [J] are used by a 100 [W] bulb in 2 minute?
A) 200 [J] B) 1200 [J] C) 12000 [J] D) 2000 [J]

6. Kinetic Energy Examples
What is the kinetic energy of a 1 [kg] mass moving at 4 [m/sec] ?
1 kg 4 m/sec
KE = ½ (1)(4)2
= 8 [J]
KE = ½ (1)(- 4)2
= 8 [J]
A) 4 [J] B) 0.25 [J] C) 2 [J] D) 8 [J]
What if the mass was going in the opposite direction
(v = - 4 [m/sec])?
1 kg
-4 m/sec
A) 4 [J] B) 0.25 [J] C) 2 [J] D) 8 [J]

7. KE Examples (cont)
 An electron has a mass of 9.1x10-31
[kg]. If it is moving at one-tenth
of the speed of light, what is it’s kinetic energy? The speed of light
is 3x108
[m/sec].
How does this compare to the 1 [kg] block moving at 4 [m/sec] ?
The electron’s velocity is v = (1/10)*(3x108
) = 3x107
[m/sec]
So, KE = ½ (9.1x10-31
)(3x107
)2
= 8.2x10-16
[J]
KE(electron) / KE(block) = 8.2x10-16
/8 = 2.6x10-17
[J]
(Wow, this is a small number. We’ll come back to this fact in a bit…)

8. Electricity
 Electricity generally refers to the flow of
charges.
 In most cases, electrons are the charges which
are actually moving.
 The units of charge is a Coulomb or simply [C].
 1 [C] = 6.25x1018
charges (such as electrons or protons)
 Alternately, 1 electron = (1 / 6.25x1018
) [C] = 1.6x10-19
[C]
 Charges are made to flow by applying a voltage
 Batteries
 Power Supplies
 Electrical generators

9. Electrical
Current
Electrical
Current
 Electrical current is the rate of flow of charges, that is [C/sec]
 The units of current are Amperes, or just Amps == [A]
 1 [A] = 1 [C/sec]
 1 [A] = 6.25x1018
charges/sec
 Lightening bolts can contain several thousand amps of current !
 Electrical current is the rate of flow of charges, that is [C/sec]
 The units of current are Amperes, or just Amps == [A]
 1 [A] = 1 [C/sec]
 1 [A] = 6.25x1018
charges/sec
 Lightening bolts can contain several thousand amps of current !

10. Electrical Energy and the Electron-Volt
 How much energy does an electron gain as it is accelerated
across a voltage? (Length of arrow is proportional to velocity)
 How much energy does an electron gain as it is accelerated
across a voltage? (Length of arrow is proportional to velocity)
-1000 [V] +1000 [V]e
 It’s energy is the product of the charge times the voltage. That is,
E = q(∆V) Charge: q is in [C]
= (1.6x10-19
)(2000) Voltage: ∆V is in [Volts] ([V])
= 3.2x10-16
[J] Energy: E is in [Joules] ([J]).
 It’s energy is the product of the charge times the voltage. That is,
E = q(∆V) Charge: q is in [C]
= (1.6x10-19
)(2000) Voltage: ∆V is in [Volts] ([V])
= 3.2x10-16
[J] Energy: E is in [Joules] ([J]).
 Because 1 electron is only a tiny fraction of a Coulomb, the energy
is also tiny ! This is a pain, but ….
 Because 1 electron is only a tiny fraction of a Coulomb, the energy
is also tiny ! This is a pain, but ….
e e e e e

11. The Electron-Volt (eV)
How much energy does an electron gain as it crosses 1 volt.
Energy = q*(∆V) = (1.6x10-19
[C]) * (1 [Volt]) = 1.6x10-19
[J]
 Since this amount of energy is so small, we define a more
convenient unit of evergy, called the “Electron-Volt”
Define the electron-Volt: 1 [eV] = 1.6x10-19
[J]
 An electron-volt is defined as the amount of energy an electron
would gain as it accelerates across 1 Volt.
 In most cases, we will use the [eV] as our unit of energy. To
convert back to [J], you need only multiply by 1.6x10-19
.
How much energy does an electron gain as it crosses 1 volt.
Energy = q*(∆V) = (1.6x10-19
[C]) * (1 [Volt]) = 1.6x10-19
[J]
 Since this amount of energy is so small, we define a more
convenient unit of evergy, called the “Electron-Volt”
Define the electron-Volt: 1 [eV] = 1.6x10-19
[J]
 An electron-volt is defined as the amount of energy an electron
would gain as it accelerates across 1 Volt.
 In most cases, we will use the [eV] as our unit of energy. To
convert back to [J], you need only multiply by 1.6x10-19
.

12. Examples
An electron is accelerated across a gap which has a voltage of 5000 [V]
across it. How much kinetic energy does it have after crossing the gap?
E = (1 electron)(5000 V) = 5000 [eV]
A proton is accelerated across a gap which has a voltage of 10,000 [V]
across it. How much kinetic energy does it have after crossing the gap?
E = (1 proton)(10000 V) = 10,000 [eV]
(we don’t refer to them as “proton-volts” !)

13. Electromagnetic Waves
• Electromagnetic (EM) waves are
another form of energy.
• In the “classical” picture, they are
just transverse waves...
The speed of EM waves
in “vacuum” is always
c = 3 x 108
[m/sec]
The wavelength (λ) is the
distance from crest-to-crest
In vacuum
c = 3x108
[m/sec] for
all wavelengths !
(~3x108
[m/sec] in air too)

14. The Electromagnetic Spectrum (EM)
Shortest wavelengths
(Most energetic)
Longest wavelengths
(Least energetic)
Recall
109
[nm] = 1 [m]
106
[µm] = 1 [m]

15.  Since all EM waves move at the same speed, they would measure
twice as many waves for the top wave as the bottom wave.
 We call the number of waves that pass a given point per second the
frequency
Frequency
Consider two waves moving to the right at the
speed c, and count the number of waves which
pass a line per second
7 waves
14 waves
1, 2, 3, 4,
5, 6, 7, 8,
9, 10 …

16. Frequency (cont)
 The frequency is usually symbolized by the greek letter, ν (“nu”)
ν == frequency
 Frequency has units of [number/sec], or just [1/sec],
or [hertz] == [hz]
 A MegaHertz [Mhz] is 1 million hertz, or 1 million waves/second!
 There is a simple relation between the speed of light, c, the
wavelength, λ, and the frequency ν.
c = λν
c = 3x108
[m/sec]

17. 10-6
[nm] * ( [ m ] )
( [nm] )
Example I
What is the frequency of a gamma-ray with λ=10-6
[nm] ?
I want to use c = λν, but we need λ in [m]…
So, first convert [nm] to [meters]
What is the frequency of a gamma-ray with λ=10-6
[nm] ?
I want to use c = λν, but we need λ in [m]…
So, first convert [nm] to [meters]
109
1
ν = c / λ = (3x108
) / (1x10-15
)
= 3 x 1023
[hz]
= 300,000,000,000,000,000,000,000 waves/sec !
That’s A LOT of waves!
= 10-15
[m]

18. Example II
What is the frequency of a gamma-ray with λ=0.5 [km] ?
First, convert [km] to [m]…
What is the frequency of a gamma-ray with λ=0.5 [km] ?
First, convert [km] to [m]…
ν = c / λ = (3x108
) / (5x102
)
= 6 x 105
[hz]
= 0.6 [Mhz]
This is AM Radio! FM Radio waves are typically around 80 Mhz. Show that
this is the case…
ν = c / λ = (3x108
) / (5x102
)
= 6 x 105
[hz]
= 0.6 [Mhz]
This is AM Radio! FM Radio waves are typically around 80 Mhz. Show that
this is the case…
0.5 [km] * ( [ m ] )
( [km] )1
103
= 5x102
[m]

19. Mass Energy
According to Einstein’s Theory of Special Relativity,
Mass is a form of Energy,
and they are related by the simple and well-known formula:
According to Einstein’s Theory of Special Relativity,
Mass is a form of Energy,
and they are related by the simple and well-known formula:
E = mc2
The units of energy, E can be expressed in [J], as before, but it is
more convenient to use the electron-volt [eV].
Recall that 1 [eV] = 1.6x10-19
[J]

20. E=mc2
E=mc2
 The important point here is that energy and mass are really
equivalent, and are related to one another by simply the speed of
light (c) squared!
 This equation implies that even if a particle is at rest, it in fact
does have a “rest-mass energy” given by this formula.

21. Example I
 What is the rest-mass energy of a 1 [kg] block in [J].
E = mc2
= (1 [kg])(3x108
[m/sec])2
= 9x1016
[J] .
This is a HUGE amount of energy stored in the rest mass!
 Really, how much energy is this?
To put it in context, you could power a 100 [Watt] light bulb for 29
million years if you could convert all of this rest mass to energy !!!!
Unfortunately, this is not possible at this point…

22. Example II
 What would be the kinetic energy of this 1 [kg] block if it were
moving at 200 [m/sec] (about 430 [mi/hr]) ?
KE = ½ (1 [kg]) (200 [m/sec])2
= 2x104
[J]
 What would be the kinetic energy of this 1 [kg] block if it were
moving at 200 [m/sec] (about 430 [mi/hr]) ?
KE = ½ (1 [kg]) (200 [m/sec])2
= 2x104
[J]
 What fraction of the rest mass energy is this ?
Fraction = (2x104
[J]) / (9x1016
[J]) = 2.2x10-13
( or 0.000000000022%)
 That is, the KE is only a tiny fraction of the rest mass energy.
Alternately, it gives you a flavor for how much energy is
bottled up in the rest mass !!!
 What fraction of the rest mass energy is this ?
Fraction = (2x104
[J]) / (9x1016
[J]) = 2.2x10-13
( or 0.000000000022%)
 That is, the KE is only a tiny fraction of the rest mass energy.
Alternately, it gives you a flavor for how much energy is
bottled up in the rest mass !!!

23. 1.5x10-10
[J] * ( [ eV ] )
( [J] )
Example III
What is the rest mass energy of a neutron, which has a mass
of 1.68x10-27
[kg]? Express the result in [eV].
E = mc2
= (1.68x10-27
[kg])(3x108
[m/sec])2
= 1.5x10-10
[J]
 Now convert to [eV].
= 9.4x108
[eV]
= 940 [MeV]
1.6x10-19
1

24. Example IV
An electron and positron (a positively-charged electron) each having
10 [keV] collide and annihilate into pure energy. How much energy
is carried away after the collision?
Total energy is conserved, so it must be the same as
before the collision. 10 keV + 10 keV = 20 keV

25. Summary
 There are many forms of energy, including:
Energy of motion
Electrical energy
Electromagnetic energy (EM waves)
Mass energy
 Energy of motion is given by KE=(1/2)mv2
 One of the most important forms of energy which we’ll deal with
is mass energy.
 Mass IS a form of energy.
 Mass can be converted into energy. If you convert all of the
mass of some object with mass M to energy, the corresponding
energy will be E=Mc2
.